第一Chern class为零的几乎复四维流形

辛同调与具有消失第一陈类的三维Besse流形

Symplectic Homology and 3-dimensional Besse Manifolds with vanishing first Chern class

本文研究了三维Besse流形的辛同调不变量，通过计算第一陈类和Robbin-Salamon指数，揭示了其与Seifert纤维空间的关联。

Almost complex manifold with Betti number $b_i=0$ except $i=0, n/2, n$

This paper studies existence of $n=4k (k>1)$ dimensional simply-connected closed almost complex manifold with Betti number $ b_i=0$ except $i=0, n/2, n$. We characterize all the rational cohomology rings of such manifolds and show they must have even Euler characteristic and even signature, which is to say the middle Betti number $b_{n/2}$ must be even. Parallel to the author's earlier work on realizing rational cohomology ring by smooth closed manifolds, we state and prove Sullivan's rational surgery realization theorem for almost complex manifold and demonstrate its application in our contex…

An obstruction for existence of codimension two contact embeddings in a Darboux chart

We prove the vanishing of the first Chern class of a codimension 2 closed contact submanifold of a cooriented contact manifold with trivial integral 2-dimensional cohomology group. Hence the first Chern class is an obstruction for the existence of codimension 2 contact embeddings in a Darboux chart. For the existence of such an embedding, we prove that a closed cooriented contact 3-manifold can be a contact submanifold of the 5-dimensional Euclidean space for a certain contact structure, if its first Chern class vanishes.

Levi非退化CR流形的陈类

Chern classes of Levi non-degenerate CR manifolds

该研究构造了满足特定陈单项式非零条件的Levi非退化CR流形，证明严格伪凸CR流形的陈类消失定理无法推广到Levi非退化情形，其基础流形不允许严格伪凸CR结构。

纽结的一个准整万有Vassiliev不变量

An almost-integral universal Vassiliev invariant of knots

定义了纽结的全陈类不变量。这是一个普遍的瓦西里耶夫不变量，它是积分“的水平上的李代数”，但它是不能表达为一个整数总和的图表。的建设是出于相似性之间的Kontsevich积分和拓扑陈特征。

关于复双曲分支覆盖的Chern数比值

On ratios of Chern numbers for complex hyperbolic branched covers

本文证明偶数维复双曲分支覆盖流形的Chern数比值不同于复双曲流形，从而回答Deraux-Seshadri问题，并表明先前构造的几乎1/4-pinched度量非Kähler。